TS EAMCET · Maths · Quadratic Equation

If $x^{2} - 3 x + 2$ is a factor of $x^{4} - a x^{2} + b,$ then the equation whose roots are $a$ and $b$ is

A $x^{2} - 9 x - 20 = 0$
B $x^{2} - 9 x + 20 = 0$
C $x^{2} + 9 x - 20 = 0$
D $x^{2} + 9 x + 20 = 0$

Verified Solution

Answer & Solution

Correct Answer

(B) $x^{2} - 9 x + 20 = 0$

Step-by-step Solution

Detailed explanation

If x2-3x+2 is a factor of x4-ax2+b, then the equation whose roots are a and b is The remainder is zero of equation x2-3x+2 x2-3x+2=0 x2-2x-x+2=0 xx-2-1x-2=0 x-2x-1=0 If x-1=0 x=1 Putting value of x in equation x4-ax2+b=0 remainder be zero 14-a12+b=0 -a+b=-1...............i…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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